ven diagram..
87=R+G-Both RG

given that ...Both = 2R/7 = 3G/7; we need to find Both/total

87= 7Both/2 + 7Both/3 - Both

Both = 18

therefore , 18/87 = 6/29 D


Corrected G in 3G/7
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You have to visualise the problem as set problem...
Given 87 Balls with Red and Green colour
So the set equation becomes; Total (Red & Green Balls) = #Red Balls + # Green Balls - Both (Red & Green)

Given is 2/7 of Red balls also are Green ==> Both ( Red and green) = \(\frac{2}{7}\) * # Red Balls
Also it is stated that 3/5 of Green balls are red, which is again stating that ==> Both ( Red and green) = \(\frac{3}{7}\) * # Green Balls

Essentially it means that #Red Balls = \(\frac{7}{2}\)* Both (Red and Green)
Also it means that #Green Balls = \(\frac{7}{3}\)* Both (Red and Green)

Now coming back to original equation Total (Red & Green Balls) = #Red Balls + # Green Balls - Both (Red & Green)

Substituting the values we got above

87= \(\frac{7}{2}*Both + \frac{7}{3}*Both - Both\)
So Both = 18

We are asked to find Both/Total =\(\frac{18}{87}\) = \(6/29\)

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